For the details on how material and waveguide profile can be created, please refer to Lessons 1 through to Lesson 9.

For the details on how a lattice can be created, please refer to Lesson 3- Photonic crystal and photonic band gap simulation and Lesson 9-FDTD Band Solver.

A unit cell has three edges a, b and c and three angles О±, ОІ and Оі between the respective edges.

Lattice points are joined by straight lines to bring out the geometry of the lattice.

A unit cell is the smallest portion of a crystal lattice, which when represented in different directions produces the complete crystal lattice.

There are seven types of unit cells: Cubic, Tetragonal, Orthorhombic, Monoclinic, Hexagonal, Rhombohedral or Trigonal and Triclinic.

Crystal lattice is a symmetrical three-dimensional structural arrangement of atoms, ions or molecules (constituent particles) inside a crystalline solid as points.

Here, D= density of a lattice, z= atomic number present in a unit cell, a= length of the side of a cube, NA= AvogradoвЂ™s Number.

Calculation of the density of unit cell.

By calculating Packing efficiency we can determine the void space. Packing efficiency means the percentage of total space filled by the particles in a unit cell.

Calculation of Packing efficiency and void space.

Relation between the length of side of the cube and radius of atoms в€ґTotal number of atoms per unit cell= 1+3= 4 atoms. (ii) 6 face-centred atoms Г— 1/2 atom per unit cell = 6 Г— 1/2 = 3 atoms. (i) For corners: 8 corners atoms Г— 1/8 atom per unit cell= 1 atom в€ґTotal number of atoms present per unit cell in bcc = 2 atoms. (ii) One atom at the body centre: 1 Г— 1= 1 atom (i) For corners: 8 corners Г— 1/8 per corner atom= 1 atom In a body-centred cubic unit cell atoms are attached at each of its corners and one atom at its body centre.

Therefore, the total number of atoms in one unit cell is 1/8*8= 1. In each of eight corners one atom remains in such position. So, only 1/8th portion of an atom belongs to a particular unit cell.

Primitive cubic unit cell has atoms only at its corner which are shared between eight adjacent unit cells among which four unit cells in the same layer and four unit cells of the upper (or lower) layer. Total Number of Atoms present in a Unit Cells Read More: Conduction of electricity in liquidsДЇourteen arrangements of three-dimensional lattices The possible variations of the Crystal system are known as Bravais Lattices. Total 14 possible three dimensional lattices are called Bravais Lattices. Primitive, Body-centred, Face-centred, End-centred Seven Primitive Unit Cells and their Possible Variations are mentioned below: There are seven different types of primitive unit cells are found such as:

End-Centred Unit Cells: In such a unit cell, one constituent particle is present at the centre of any two opposite faces, as well as its corners.

Face-Centred Unit Cells: Such a unit cell contains one constituent particle present at the centre of each face, as well as its corners.

Body-Centred Unit Cells: Such a unit cell contains one constituent particle (atom, molecule or ion) at its body-centre as well as its every corners.

Read More: Physical and Chemical Classification Of MatterД¬entred unit cells are classified into three types: (b) Centred Unit Cells: A centred unit cell contains one or more constituent particles which are present at positions besides the corners. (a) Primitive Unit Cells: In a primitive unit cell constituent particles are present only on the corner positions of a unit cell. Unit cells are generally classified into two categories such as primitive and centred unit cells. Read More: Classification of Crystalline Solids Therefore, a unit cell is characterised by six parameters such as a, b, c and О±, ОІ, Оі. (ii) The angles held by the edges are О± (between b and c) ОІ (between a and c) and Оі (between a and b). These edges can form different angles, they may be mutually perpendicular or may not. (i) The dimensions are measured along the three edges, a, b and c. The smallest portion of a crystal lattice which repeats in different directions to form the entire lattice is known as Unit cell. (c) Lattice points are joined by straight lines to construct the geometry of the lattice. (b) An atom, a molecule (group of atoms) or an ion is represented by each point in a crystal lattice. (a) Each point in a lattice is known as a lattice point or lattice site. The characteristics of a crystal lattice are: Read More: Difference between Cations and Anions

Define lattice